Vortex Generation in Cyclically Coupled Superfluids and the Kibble-Zurek Mechanism

We study theoretically the generation of cyclic supercurrent among three superfluids coupled by the Josephson Junctions. Depending on the initial relative phases between superfluids, Josephson current flows cyclically through the superfluids to create a quantized vortex. Reducing the coupling strength changes the motion from periodic to chaotic, thus suppressing the cyclic current. Applying this result to the Kibble-Zurek mechanism, the probability of the vortex generation via this mechanism is modified from the simple estimate given by the geodesic rule. We compare our results with the Lancaster, Grenoble and Helsinki experiments.